Interesting, I guess that is not how I view it. To me, wizards learn magic through research and study. That is their thing. A sorcerer has it in their blood, they can only develop within the limits of that (in fact I think they should have more limited spells based on their bloodline). If they wanted to "research" other magic, that would be akin to multiclassing into a wizard. Similar for the warlock. So sure, a warlock or sorcerer could learn other spells; however, that process essential makes them a wizard. A wizards is someone who learns spells via research and study. So by learning that way, you are learning the wizard way.
That beings said, I don't hate your view. It is just different from how I construct my campaign worlds and that is OK.